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statistical sampling to auditing

Questions and Answers of Statistical Sampling To Auditing

19 You are assigned to direct a study on your campus to determine the factors that relate to strong academic performance at the school.a) Describe how you might select a sample of 100 students for
20 Quota sampling is a method used when. for example, an interviewer stands at a street corner and conducts interviews until obtaining a quota in various categories representing the relative sizes of
21 in 1995 in the United Kingdoin. the Equality Code used by the legal profession added a section to make members more aware of the dangers of sexual harassment It states that "esearch for the Bar
22. When the Yankelovich polling organization asked, "Should laws be passed to eliminate all possibilities of special interests giving huge sums of money to candidates" 80% of the sample answered
23 Crosson (1994, p 168) describes an analysis of published medical studies involving treat- ments for heart attacks. In the studics having randomization and strong controls for bias. the new therapy
24 In each of the following situations, evaluate whether the method of sample selection is appropriate for obtaining information about the population of interest How would you improve the sample
25. Refer to the previous exercise. Repeat for the following scenarios:a) A principal in a large high school is interested in student attitudes toward a proposed general achievement test to determine
26 You plan to sample from the 5000 students at your college in order to compare the pro- portions of men and women who believe that women should have the right to an abortion.a) Explain how you
27 In a systematic random sample. every subject has the same chance of selection. but the sample is not a simple random sample. Explain why, by showing that every possible saru- ple of size n is not
28. 1 need to collect data for a sample of residents of registered nursing homes in my state. 1 obtain from the state a list of all nursing homes, which I number from 1 to 317 Beginning randomly, I
1 According to the Bureau of the Census (Current Population Reports). in 1994 in the United States there were 23.6 million households with one person, 31.2 million with two persons, 169 million with
2 According to News America Syndicate in 1986 the number of followers of the world's major religions were 835 million for Christianity, 420 million for Islan, 322 million for Hinduism. 300 million
3. Refer to Table 3.1. Use software to construct a histogram for these data. using its default method of forming intervals Describe the shape of the distribution, and construct the corresponding
4. Table 311 shows the number (in millions) of the foreign-born population of the United States in 1990. by place of birth.a) Construct a relative liequency distribution.b) Plot the data in a bar
5 A researcher in an alcoholism treatment center. interested in summarizing the length of stay in the center for first-time patients, randomly selects ten records of individuals insu- tutionalized
6 The 1994 General Social Survey asked respondents "How often do you read the newspa- per? The possible responses were (every day, a few times a week once a week, less than once a week. never). and
7 Table 3.12 summanzes responses of 1250 subjects in the 1991 General Social Survey to the question. "About how often did you have sex during the last 12 months?"a) Construct a bar graph, and
8. The 1991 General Social Survey asked respondents, "How many sex partners have you had in the last 12 months?" Table 3.13 shows results for 637 respondents.a) Calculate and interpret the median and
9. For 1992, the statewide muumber of abortions per 1000 wonen 15 to 44 years of age, for states in the Pacific region of the United States, were: Washington, 33, Oregon, 16: Cal- ifornia. 304;
10. For 1993. Table 91 in Chapter 9 shows data on the statewide violent crime rate per 100,000 population. In this exercise. do not use the observation for D.Ca) Using the intervals 0-100, 100-200,
11. Refer to the preceding problem. Table 3.14 shows part of a computer printout for analyz- ing the data, the first colunin refers to the entire data set, and the second column deletes the
12. In 1992 in the United States, the median family income was $38 909 for white families. $21.161 for black families, and $23.901 for Hispanic families (C.S Bureau of the Census. Current Population
13 Table 3.15 shows 1994 female economic acu vity for countries in South America.a) Construct a back-to-back stem and leaf plot of these values contrasted with those from Eastern Europe in Table 3 6.
14 According to the US Bureau of the Census. Current Population Reports, in 1994 the median household income was $32.368 for whites and $18,660 for blacks, whereas the mean household income was
15 Refer to the previous exercise. The results refer to 57.9 million white households and 8.0 million black households.a) Find the overall mean income.b) If the mean income equals $30,291 for 59
16. For towns with population size 2500 to 4599 in the US. Northeast in 1994. the mean salary of chiefs of police was $37.527, and the median was $30.500 (The Municipal Year Book 1995. Washington.
17. According to the National Association of Home Builders. the US nationwide median selling price of hoines sold in 1995 was $118,000.a) Would you expect the mean to be larger, smaller. or equal to
18. The 1990 General Social Survey asked respondents, "During the past 12 months, how many people have you known personally that were victims of homicide." Table 3.16 show's a computer printout from
19 The Human Development Index (HDI) has three components life expectancy at birth. cducational attainment, and income. It ranges from 0 to 1, with higher values representing greater development. In
20 According to Statistical Abstract of the United States, 1995, average salary (in dollars) of secondary school classroom teachers in 1994 in the Unued States varied among states with a five-number
21 Consider the data in Table 3.8 on the number of people you know who have committed suicide. The mean equals .145, and the standard deviation equals .457 Froin the results reported in the table,
22 Why is the median sometimes preferred over the mean as a measure of central tendency? Give an example to illustrate your answer.
23. Why is the mean sometimes preferred over the median? Give an example to illustrate your answer
24 Give an example of a vanable for which the mode applies, but not the mean or median.
25. A group of high school students takes an exain The mean score for the boys is 65. and the median is 75. Both the mean and the median score for the girls is 70. How can you explain the large
26. During the spring semester of 1995 at the University of Flonda, coinputer usage of stu- dents having accounts on a mainframe computer at the university was summarized by a mean of 1921 and a
27. Refer to Problem 3.26. The five-number summary of these data was minimum = 4, Q1= 256, median = 530. Q3 = 1105, and maximum = 320,000. What does this suggest about the shape of the distribution?
28 Residential electrical consumption in March 1994 in Gainesville. Florida, had a mean of 780 and a standard deviation of 506 kilowatt-hours (Kwh). The minimum usage was 3 Kwh and the maximum was
29. Residential water consumption in March 1994 in Gainesville, Flonda, had a mean of 7.1 and a standard deviation of 6.2 (thousand gallons) What shape do you expect this distn- bution to have? Why"
30 For each of the following. sketch roughly what you expect a histograin to look like, and explain whether the mean or the median would be greater. Also sketch box plots for cases (a) and (c) that
31 For each of the following vanables. indicate whether you would expect its relative fre- quency histogram to be bell-shaped, U-shaped, skewed to the nght, or skewed to the left. For parts (a), (b),
32. Give examples of social science variables having a distribution that you would expect to bea) Approximately syinmetricb) Skewed to the rightc) Skewed to the leftd) Bimodale) Skewed to the right,
33. A recent Roper organization survey asked. "How far have environmental protection laws and regulations gone?" For the possible responses not far enough. about right, and too far, the percentages
34. A company conducts a study of the number of miles traveled asing public transportation by its employees during a typical day. A random sample of ten employees yields the fol- lowing values (in
35. To measure variation:a) Why is the standard deviations usually prefened over the range?b) The IQR is sometimes preferred to when there are some extreme outliers Why?
36 In the mid-1980s. the General Social Survey asked respondents how many close friends they had. For a sample of size 1467. the mean was 7.4 and the standard deviation was 110. The distribution had
37. In 1994 the General Social Survey asked, "On the average day, about how many hours do you personally watch television" Of 1964 responses, the mode was 2, the inedian was 2, the inean was 28, and
38 For an exam given to a class, the students' scores ranged from 35 to 98, with a incan of 74. Which of the following is the most realistic value for the standard deviation? 1.12. 60, -10" Why"
39 The sample mean for a data set equals 80 Which of the following is an impossible value for the standard deviation? 200,0 -20.
40 According to a recent report from the US National Center for Health Statistics, feinales with age between 25 and 34 years have a bell-shaped distribution on height, with mean of 65 inches and
41 In a large northern city, monthly payinents to people on welfare last year were observed to have approximately a bell shape with mean $700 and standard deviation $100 Give a range of values within
42 For the WWW data on number of times a week reading a newspaper, referred to in Prob- lem 1.7, Figure 3.18 shows a computer printout of the stein and lead plot and the box plot.a) From the box
43 Suppose the distribution of the prices of new homes built in the United States in 1996 was approximately bell-shaped, with a mean of $120.000 and a standard deviation of $40,000a) Describe the
44 In 1993, the five-number sunniary for the statewide percentage of people without health insurance had a minimum of 8.7% (Wisconsin). Q1 = 11 9, Med = 13.4, Q3 = 17.8, and maximum of 23 9%
45 Refer to Problem 3.20. Construct a box plot for these data Are there any apparent out- liers?
46 The distribution of high school graduation rates in the United States in 1993 had a mini- anum value of 64.3 (Mississippi), lower quartile of 73 9, median of 76.75. upper quartile of 80.1. and
47. In your library, find the percentage of the vote that Bill Clinton received in each state in the 1996 presidential election.a) Prepare a stein and leaf plot. Are there any apparent oudiers?b)
48. Refer to Problein 3.10a) Using the data set without D.C., find the quarules and the interquartile rangeb) According to the definition of an outlier in terms of the IQR, are any of the
49. What is the difference between the descriptive measures symbolized bya) Y and ?b) s and ?
50. For the WWW data file (Problem 1.7), use computer software to conduct graphical and numerical suminaries fora) distance from hoine town,b) weekly hours of TV watching.c) weekly number of times
51. Refer to the data file yon created in Problem 1.7 For variables chosen by your instructor, conduct descriptive statistical analyses Prepare a report, interpreting and summanzing your findings.
52. Refer to the data in Table 9.1 on poverty rates. Using methods of this chapter, summarize these data Prepare a report, graphically displaying the data and summarizing the central tendency and
53. The number of therapeutic abortions in 1988 in Canada, per 100 live births, is shown in Table 3.17 Using methods of this chapter, present a descriptive statistical analysis of these data,
54. Refer to Problem 3.19. Table 3.18 shows the HDI ratings for African countries Using graphical and numerical methods of this chapter, summarize HDI for these countries, and compare to the
55. Obtain data on statewide murder rates from the latest edition of Statistical Abstract of the United Statesa) Analyze the data using the graphical and numerical methods of this chapter.b) Use
56. During the strike of professional baseball players in 1994, two quite different numbers were reported for the central tendency of players annual salanes. One was $1.2 million and the other was
57 In 1986. the US. Federal Reserve sampled about 4000 households to estimate overall net worth of a family. Excluding some outliers of extremely wealthy individuals. they reported the summaries
58. According to a recent report from the U.S. National Center for Health Statistics. for males with age 25-34 years. 2% of their heights are 64 inches or less. 8% are 66 inclies or less. 27% are 68
59. Grade point averages of graduating seniors at the University of Rochester are approxi- mately bell-shaped in distribution ranging from 20 to 4.0 with a mean of about 3.0. Us- ing the fact that
60. In Canada in 1981. for the categories Catholic. Protestant, Eastern Orthodox. Jewish. None. Other for religious affiliation, the relative frequencies were 47 3%, 41.2%. 15%. 1.2%. 7.3%, 1.5%
61. The 1991 General Social Survey asked whether having sex before manage is always wiong, almost always wrong, wrong only sometimes, not wrong at all. The response counts in these four categories
62 Ten families are randomly selected in Florida and another ten families are randomly se- lected in Alabaina Table 3.19 provides summary information on incan family income The mean is higher in
63 Refer to Problem 3.10. Explain why the mean of these 50 measurements is not necessarily the same as the violent crime rate for the entire U.S. population.
64 The mican and standard deviation of a sample may change if data are rescaled For a sain- ple with mean Y, adding a constant c to each observation changes the mean to Y +c. and the standard
65. The results of the study described in Problem 3.34 are to be reported in a French news- paper. The ten measurements are converted to kilometer units (1 inile 1.6 kilometers). Report the incan and
66 *. The crude death rate is the number of deaths in a year. per size of the population. mul- tiplied by 1000 According to the U.S. Bureau of the Census in 1995 Mexico had a crude death rate of 4.6
67 "The sample means fork sets of data with sample sizes m are Y. Y...Y. Show that the overall saniple mean for the combined data set is Interpret as a weighted average of Y. .....Interpret as a
68. Show that E();-) must equal 0 for any collection of measureinents Y, Y....Y-
69. The Russian inathematician Tchebysheff proved that for any real number > 1, the pro- portion of the measurements that fall more than & standard deviations from the mean can be no greater than i
70. The least squares property of the mean states that the data fall closer to than to any other real numberc. in the sense that the sum of squares of deviations of the data about their mean is
1 Let the number of people you have known personally that have committed suicide within the past 12 months According to recent General Social Surveys, the probabilities for the potential values of Y
2 Let = number of people you lave known personally who came down with AIDS Sup- pose Table 3.9 refers to the population of interesta) Construct the probability distribution for Yb) Find the mcan of
3. Five students, Ann. Betty. Clint. Douglas, and Edward. are rated equally qualified for ad- mission to law school. ancad of other applicants However, all but two positions have been filled for the
4. Refer to the previous exercise. Construct the probability distribution of X = number of females admitted. when three of the five students are randomly selected for admission. Find the mean of the
5 Let be the outcome of selecting a single digit from a random number table.a) List the possible values for Yb) Construct the probability distribution for) (This type of distribution is called a uni-
6. In a statewide lottery, one can buy a ticket for $1. With probability .0000001. one wins a million dollars (S1,000,000). and with probability .9999999 one wins nothing (SO).a) Let Y denote the
7. For a normal distribution. find the probability that an observation isa) At least one standard deviation above the mean.b) At least one standard deviation below the mean.c) At least .67 standard
8. For a normally distributed variable, venly that the probability betweena) - and equals .68b) -1.960 and + 1.960 equals .95. c)-30 and -30 equals.997. -d) 670 and .670 equals.50
9 Find the -value for which the probability that a normal variable exceeds so equalsa) .01b) .025 c).05 d).10e) .25 1).50
10. Find the z-value such that the interval from -zo to +20 containsa) 50%.b) 90%.c) 95%,d) 98%.e) 99% of the probability for a nonnal distribution.
11. Find the z-values corresponding to thea) 90th,b) 95th,c) 98th. andd) 99th percentiles of a normal distribution
12. Show that if is the number such that the interval from 0 to +co contains 90% of a normal distribution, then u+zo equals the 95th percentile.
13. If is the positive number such that the interval from u-go to + contains 50% of a normal distribution, then which percentile isa) +b) zo? Find this value of :. Using this result, explain how to
14. An observation is .50 standard deviations below the mean on a normally distributed vari- able. What proportion of the data fall below that observation? Above it?
15 What proportion of a normal distribution falls in the following rangesa) Above a z-score of 2.10.b) Below a z-score of -2 10.c) Above a z-score of -2.10.d) Between-scores of -2.10 and 2 10.
16. Find the z-score for the number that is less than ouly 1% of the values of a nonnal distn- bution
17. Find the z-scores for the lower and upper quartiles of a normal distribution.
18. According to Current Population Reports, self-employed individuals in the United States in 1990 worked an average of 44.6 hours per week. with a standard deviation of 14.5. Assuming this variable
19. The Mental Development Index (MDI) of the Bayley Scales of Infant Development is a standardized measure used in longitudinal follow-up of high-risk infants. It has approxi- mately a normal
20. For 5459 pregnant women using Aarhus University Hospital in Denmark in a two-year period who reported information on length of gestation until birth, the mean was 2819 days. with standard

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